# 4 Gridded Prime Numbers

You have the first four prime numbers ($2$,$3$,$5$ and $7$) which are gridded and shown as below: You are trying to get highest total score you can reach with arranging the numbers by rotating (no reflection allowed) them without overlapping them on each other.

The total score is calculated how many lines are joint after arranging and multiplying how many joints you got with the actual prime number and take the sum of all gridded prime number scores at the end. For example, if this question was asked to arrange the first two prime numbers ($2$ and $3$), the answer would be as below: Since there are 8 lines of the grid are touched with each other, the total score would be $2\times8+3\times8=40$ which is the maximum score you can get with $2$ and $3$.

Note: I am very sorry to let you know there is better answer than 172. That's totally my mistake!

• It is definitely not clear how score is computed. Ah Got It, when you mentioned 8 lines you should have noted that the picture is actually also 8 lines high. XD Sep 13 '16 at 10:32
• i'm sorry...did you mean to say "there is no better answer than 172"? Jun 5 '17 at 20:08

I have 172, with the correct tiles.

• also, just rotate the 2 clockwise 90 degrees for an extra 5 points Sep 10 '16 at 21:27
• For anyone interested in trying to beat this, I made a spreadsheet to make it easier to play around with. Make a copy for yourself and try to beat 172! May 30 '17 at 15:29
• Thanks for that spreadsheet. I tried lots of combinations but I have no idea how to get more than 172. May 30 '17 at 21:53
• @GentlePurpleRain Nicely made! I wrote a small macro to utilize the spreadsheet and brute-force possible solutions. Can't get past 172. Jun 5 '17 at 20:06

I believe the maximum is

172

Otherwise I think the maximum cannot be found by a greedy approach (trying to maximize the contact point between numbers.

My alternative solution to Matsmath:

• Isn't your solution the same as mine, just rotated 180 degrees (essentially: turned upside down)? Sep 23 '16 at 8:56
• oh men, you are right. I spent 1 hour on that - Sep 23 '16 at 10:56

I got

176

With this formation:

• 7 is wrong shape.
– Oray
Jun 2 '17 at 18:23
• Alright, how about now? Edited the answer Jun 2 '17 at 18:28
• @Oray interchanged 5 and 2 because 2's rotation just did not seem right. Score is still the same. Jun 2 '17 at 18:35
• How is this accepted and bountied when the 7 is reflected, which the puzzle statement expressly does not allow? @Oray
– Rubio
Jun 2 '17 at 23:10
• @Rubio that's totally my mistake sorry :/
– Oray
Jun 3 '17 at 5:52

I have

$166$

With $2\times 6 + 3\times 8 + 5\times 12 + 7\times 10 = 166$

• that is $6*9 + 4*12 + 8*8 = 166$ Sep 13 '16 at 9:49
• Yes it should be $166$, I had missed one of the seven edges in the count. Sep 13 '16 at 9:58

I got

182 146

With this formation:

EDIT: Miscalculated the score.